She was 'burning for' a chance to prove herself. [=she wanted very much to get a chance to prove herself]
('humorous') “We were talking about you last night.” “That explains why I 'felt my ears burning'.”
She was 'burning with' anger at his rudeness. [=she was very angry because of his rudeness]
(..) Can I ask what you got it for? Since it bears on this conversation, I got it for pulling a -pound man out of a burning tank. So when a man tries to rescue another man, he's a hero, but when he tries to rescue a woman, he's just gone soft. Could you have (..)1997 G.I. Jane